{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Z7CDOBUEPF3NINLOAJLAWE47YA","short_pith_number":"pith:Z7CDOBUE","canonical_record":{"source":{"id":"1502.04063","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-02-12T06:25:22Z","cross_cats_sorted":[],"title_canon_sha256":"7ba1c1b054525ab99907759dd1a4c8a9c93c7fd1d410eda216f5bbbdfed08065","abstract_canon_sha256":"9e89b3179eceeda159038f16268a1064cc46a304a2b93b933ca862bf97ad7d5a"},"schema_version":"1.0"},"canonical_sha256":"cfc43706847976d4356e02560b139fc028f2d7c5576953b8920e93e03512b0e9","source":{"kind":"arxiv","id":"1502.04063","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04063","created_at":"2026-05-18T00:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04063v3","created_at":"2026-05-18T00:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04063","created_at":"2026-05-18T00:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"Z7CDOBUEPF3N","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z7CDOBUEPF3NINLO","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z7CDOBUE","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Z7CDOBUEPF3NINLOAJLAWE47YA","target":"record","payload":{"canonical_record":{"source":{"id":"1502.04063","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-02-12T06:25:22Z","cross_cats_sorted":[],"title_canon_sha256":"7ba1c1b054525ab99907759dd1a4c8a9c93c7fd1d410eda216f5bbbdfed08065","abstract_canon_sha256":"9e89b3179eceeda159038f16268a1064cc46a304a2b93b933ca862bf97ad7d5a"},"schema_version":"1.0"},"canonical_sha256":"cfc43706847976d4356e02560b139fc028f2d7c5576953b8920e93e03512b0e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:03.908377Z","signature_b64":"HQrl0OXG13gnNFqRYnfXqIpzc2mRGejq5RjJD7nmM8k4CGkqr4n227wNx/gO3vck3MPN6WAyw81TboRxK+0eBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfc43706847976d4356e02560b139fc028f2d7c5576953b8920e93e03512b0e9","last_reissued_at":"2026-05-18T00:54:03.907878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:03.907878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.04063","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"etVKgR7ABjcauanRJvKzw6em3QIqiQd2wENPzma0sg4ZpUjz1Nos6q0S6MKqLcG4i+m2Qr5Lemmt25Ax6vBrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:09:34.508824Z"},"content_sha256":"18200084fbbe6a25a13d90c3e1f53c355fb7202bfd7629db689e930ddc059fb2","schema_version":"1.0","event_id":"sha256:18200084fbbe6a25a13d90c3e1f53c355fb7202bfd7629db689e930ddc059fb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Z7CDOBUEPF3NINLOAJLAWE47YA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear Map of $D$-Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Aleks Kleyn","submitted_at":"2015-02-12T06:25:22Z","abstract_excerpt":"Module is effective representation of ring in Abelian group. Linear map of module over commutative ring is morphism of corresponding representation. This definition is the main subject of the book.\n  To consider this definition from more general point of view I started the book from consideration of Cartesian product of representations. Polymorphism of representations is a map of Cartesian product of representations which is a morphism of representations with respect to each separate independent variable. Reduced morphism of representations allows us to simplify the study of morphisms of repre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04063","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cXmjAg/5lF/pW9PhvApc/rWdSpVJTP8x7VCGxlHUTzgNy2HHKOvjs3X5ZF2Abmh8fyrMHn2+zZYu6Z+Tcv5pAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:09:34.509508Z"},"content_sha256":"298fb84fbf7ebba6c677ff1ecb9d61b3e73c9e9dc7d5d14ac7f15408b5d1a23f","schema_version":"1.0","event_id":"sha256:298fb84fbf7ebba6c677ff1ecb9d61b3e73c9e9dc7d5d14ac7f15408b5d1a23f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z7CDOBUEPF3NINLOAJLAWE47YA/bundle.json","state_url":"https://pith.science/pith/Z7CDOBUEPF3NINLOAJLAWE47YA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z7CDOBUEPF3NINLOAJLAWE47YA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T06:09:34Z","links":{"resolver":"https://pith.science/pith/Z7CDOBUEPF3NINLOAJLAWE47YA","bundle":"https://pith.science/pith/Z7CDOBUEPF3NINLOAJLAWE47YA/bundle.json","state":"https://pith.science/pith/Z7CDOBUEPF3NINLOAJLAWE47YA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z7CDOBUEPF3NINLOAJLAWE47YA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z7CDOBUEPF3NINLOAJLAWE47YA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9e89b3179eceeda159038f16268a1064cc46a304a2b93b933ca862bf97ad7d5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-02-12T06:25:22Z","title_canon_sha256":"7ba1c1b054525ab99907759dd1a4c8a9c93c7fd1d410eda216f5bbbdfed08065"},"schema_version":"1.0","source":{"id":"1502.04063","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04063","created_at":"2026-05-18T00:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04063v3","created_at":"2026-05-18T00:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04063","created_at":"2026-05-18T00:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"Z7CDOBUEPF3N","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z7CDOBUEPF3NINLO","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z7CDOBUE","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:298fb84fbf7ebba6c677ff1ecb9d61b3e73c9e9dc7d5d14ac7f15408b5d1a23f","target":"graph","created_at":"2026-05-18T00:54:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Module is effective representation of ring in Abelian group. Linear map of module over commutative ring is morphism of corresponding representation. This definition is the main subject of the book.\n  To consider this definition from more general point of view I started the book from consideration of Cartesian product of representations. Polymorphism of representations is a map of Cartesian product of representations which is a morphism of representations with respect to each separate independent variable. Reduced morphism of representations allows us to simplify the study of morphisms of repre","authors_text":"Aleks Kleyn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-02-12T06:25:22Z","title":"Linear Map of $D$-Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04063","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:18200084fbbe6a25a13d90c3e1f53c355fb7202bfd7629db689e930ddc059fb2","target":"record","created_at":"2026-05-18T00:54:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9e89b3179eceeda159038f16268a1064cc46a304a2b93b933ca862bf97ad7d5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-02-12T06:25:22Z","title_canon_sha256":"7ba1c1b054525ab99907759dd1a4c8a9c93c7fd1d410eda216f5bbbdfed08065"},"schema_version":"1.0","source":{"id":"1502.04063","kind":"arxiv","version":3}},"canonical_sha256":"cfc43706847976d4356e02560b139fc028f2d7c5576953b8920e93e03512b0e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfc43706847976d4356e02560b139fc028f2d7c5576953b8920e93e03512b0e9","first_computed_at":"2026-05-18T00:54:03.907878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:03.907878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HQrl0OXG13gnNFqRYnfXqIpzc2mRGejq5RjJD7nmM8k4CGkqr4n227wNx/gO3vck3MPN6WAyw81TboRxK+0eBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:03.908377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04063","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18200084fbbe6a25a13d90c3e1f53c355fb7202bfd7629db689e930ddc059fb2","sha256:298fb84fbf7ebba6c677ff1ecb9d61b3e73c9e9dc7d5d14ac7f15408b5d1a23f"],"state_sha256":"85268b1a38269cb82028bda2968dc58e6f40d0e35e1903cb12509552c8d86b6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TebULPgItYpNUYAPKhKQEP2hdSoaojejOkU7nHKm7tXSs72vFjX88dtI97aa2l12mvmQEo+Og7k4+1Ol2gpwAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:09:34.513888Z","bundle_sha256":"694567153abff3b5f6a5dc077ca5232b85bb7764da7d362173e1050ef54de1ee"}}